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Volume 22, Issue 4
Minimal Hypersurfaces in Hyperbolic Spaces

Jun Sun

DOI: 10.4208/jpde.v22.n4.4

J. Part. Diff. Eq., 22 (2009), pp. 352-361.

Published online: 2009-11

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  • Abstract

In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 (1982), pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method.

  • Keywords

Hyperbolic space minimal hypersurfaces mean curvature flow comparison theorem

  • AMS Subject Headings

35K55 53A10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-22-352, author = {Jun Sun }, title = {Minimal Hypersurfaces in Hyperbolic Spaces}, journal = {Journal of Partial Differential Equations}, year = {2009}, volume = {22}, number = {4}, pages = {352--361}, abstract = {

In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 (1982), pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v22.n4.4}, url = {http://global-sci.org/intro/article_detail/jpde/5262.html} }
TY - JOUR T1 - Minimal Hypersurfaces in Hyperbolic Spaces AU - Jun Sun JO - Journal of Partial Differential Equations VL - 4 SP - 352 EP - 361 PY - 2009 DA - 2009/11 SN - 22 DO - http://doi.org/10.4208/jpde.v22.n4.4 UR - https://global-sci.org/intro/article_detail/jpde/5262.html KW - Hyperbolic space KW - minimal hypersurfaces KW - mean curvature flow KW - comparison theorem AB -

In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 (1982), pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method.

Jun Sun . (2009). Minimal Hypersurfaces in Hyperbolic Spaces. Journal of Partial Differential Equations. 22 (4). 352-361. doi:10.4208/jpde.v22.n4.4
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